In a medium saucepan, heat the 6 tablespoons of olive oil over medium heat. Add the shallots, season lightly with salt, and cook, stirring, until the shallots just begin to color, about 4 minutes. Add the mushrooms, thyme, and the remaining 1 teaspoon olive oil, and cook, stirring occasionally, until the mushrooms release their liquid, about 2 minutes. Add the Chicken Reduction, bring to a boil, then reduce to a simmer. Cook, stirring occasionally, until the liquid is reduced by half and has a saucy consistency, 2 to 3 minutes. Stir in the preserved truffles (if using). If the mixture thickens too much -- you want the mushrooms to be swimming in the sauce but there should be a mushroom in every bite -- add 2 tablespoons of the Chicken Reduction to thin it out a bit. Stir in the chives and crushed red pepper.
Divide the Creamy Polenta among serving bowls. Top with the mushrooms and their cooking liquid and serve immediately.
Heat a convection oven to 425 degrees F or a conventional oven to 450 degrees F.
Rinse the chicken bones and pat them dry. Spread them out on two rimmed baking sheets in a single layer with a little room between the bones. Roast until golden brown, about 1 hour, flipping and turning the bones every 15 minutes or so.
In a large stockpot, heat the olive oil over medium heat. Add the rosemary and garlic and cook, stirring, until fragrant, about 1 minute. Add the celery, onion, and carrot, and cook, stirring occasionally, until the vegetables are well browned, about 10 minutes. Add the tomatoes, and cook, stirring, until some of the juices evaporate, 2 to 3 minutes. Add the wine and cook until almost all of it has evaporated. Add the chicken bones (with juices and drippings) to the stockpot, then add enough water to cover everything by about 2 inches (about 6 quarts). Increase the heat to medium-high, bring to a boil, then reduce the heat to medium to cook at a gentle simmer, stirring often to break up the bones and emulsify the fat, until the chicken is falling off the bones and the stock has a full flavor, 2 to 2 1/2 hours.
Remove the chicken bones and strain the broth several times through a chinois or other fine-mesh strainer. If you want to make and use the reduction right away, spoon off any visible fat floating on top of the stock. Otherwise, chill the stock until the fat solidifies on top, and then scrape off and discard most of it.
Pour the defatted stock into a saucepan and bring to a boil over high heat. Reduce the heat slightly so the stock is not boiling so furiously. As the stock simmers, some of it will remain on the sides of the saucepan; use a spoon or ladle to pour some of the stock over this to deglaze it. (This will further increase the intensity of the flavor.) Continue simmering until the stock has darkened, thickened, and reduced to about 4 cups, about 30 minutes. The reduction can be refrigerated for 3 days or frozen for up to 2 months. Yield: 4 cups
In a large, heavy-based saucepan over medium-high heat, heat the cream and milk until warm, about 5 minutes. Whisk in the salt and keep whisking until the liquid is very frothy (like a cappuccino) and hot. While still whisking, slowly rain the polenta into the pot. Continue to whisk until the granules swell, about 8 minutes. At this point, switch to a wooden spoon to stir the polenta. (It will get too thick for the whisk.) Keep stirring until the polenta has begun to thicken, about 5 minutes. Turn the heat down to medium and cook until it evenly begins to bubble. Reduce the heat to low, cover with a tight-fitting lid, and cook, stirring every 10 to 15 minutes, until cooked through and the liquid has reduced, about 1 1/2 hours. The polenta might look "done" sooner, but it does continue to soften, so be patient. During this time, a skin might form on the bottom of the pan, which is fine.
Just before serving, raise the heat to medium-high, stir in the butter and the cheese, and cook, stirring, until the butter is melted, then take the pot off the heat. If the polenta looks thin, don't worry, as it will thicken as it cools. Yield: 8 to 10 servings
If you don't want to make, or don't have time to make, this chicken reduction, experiment with some of the commercial chicken reductions out there. One that I have tried with success is called Glace de Poulet Gold, by More Than Gourmet brand. A classic reduced chicken stock, it can be reconstituted to get a flavorful chicken reduction that, while not exactly what I make, is exceedingly convenient. You can find it at most supermarkets as well as at specialty food markets.
Adapted from "Scarpetta Cookbook" by Scott Conant. Copyright Houghton Mifflin Harcourt Publishing Company 2013. Provided courtesy of Scott Conant. All rights reserved.